Excerpt from The Small Dispersion Limit of the Korteweg-Devries Equations We also show that leads, in an appropriate weak sense, to a limit. In Section 3 we show that Q is continuous in a weak sequential topology, and that the space of admissible functions is compact in that topology. We further show that Q is a strictly convex function; since the admissible functions form a convex set, this implies not only that the minimum of Q is taken on at a unique function, but that this function is the only one which satisfies ...
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Excerpt from The Small Dispersion Limit of the Korteweg-Devries Equations We also show that leads, in an appropriate weak sense, to a limit. In Section 3 we show that Q is continuous in a weak sequential topology, and that the space of admissible functions is compact in that topology. We further show that Q is a strictly convex function; since the admissible functions form a convex set, this implies not only that the minimum of Q is taken on at a unique function, but that this function is the only one which satisfies variational conditions. The variational conditions are then converted to a riemann-hilbert problem, i.a. To the problem of determining an analytic function of class Hp in the upper half plane whose real and imaginary parts are prescribed on alternate intervals of the real axis. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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